MAT: Mathematics

MAT 500. Fundamentals of Applied Mathematics. 3 Credits.

This course is designed to provide an intense review of the core concepts essential to the study of applied mathematics. Topics include the main theorems of differential and integral calculus; techniques and theorems of vector analysis; sequences and power series; complex arithmetic and elementary complex-valued functions; first-order, second-order, and systems of linear differential equations; matrix algebra and vector spaces. The computer algebra systems Matlab and Mathematica will be introduced as computational tools for these topics.

MAT 503. History Of Mathematics. 3 Credits.

This course will cover selected topics from the history of mathematics. Many great mathematicians will be studied including Hippocrates, Euclid, Archimedes, Heron, Cardano, Newton, the Bernoulli Brothers, Euler, Gauss, and others. Mathematics problems will be approached using the methods and knowledge of the era studied. A solid background in undergraduate mathematics is required.

MAT 513. Linear Algebra. 3 Credits.

This course covers advanced topics in linear algebra. The basic notions of vector space, linear transformation, and determinant will be reviewed and used to study eigenspace theory, inner-product spaces, invariant subspaces, and various decompositions. Several applications throughout the course will be emphasized.

MAT 514. Theory of Numbers. 3 Credits.

This course covers divisibility, linear congruence, the Chinese Remainder Theorem, Euler's phi function, primitive roots, and quadratic reciprocity. Additional topics may include public-key cryptography, Diophantine equations, continued fractions, and the distribution of primes.

MAT 515. Algebra I. 3 Credits.

This course provides a rigorous study of groups, group homomorphisms, products and sums, structure of groups, rings and their homomorphisms, ideals, and factorization properties.

MAT 516. Algebra II. 3 Credits.

This course is a continuation of MAT 515. Topics covered include fields, field extensions, and Galois theory. Additional topics such as modules or basic homological algebra may be explored as time permits.

MAT 516 Prerequisite: Successful completion of MAT 515, with a minimum grade of C-.

MAT 517. Topics in Algebra. 3 Credits.

This is an advanced topics course in abstract algebra. Topics may be chosen from group theory, ring theory, Lie theory, combinatorial algebra, algebraic geometry, homological algebra, and/or representation theory.

MAT 521. Discrete Mathematics & Graph Theory. 3 Credits.

Topics from Discrete Mathematics including the study of logic, sets, relations, and counting will be introduced. Graphs and Graph Theory will be discussed, including Eulerian and Hamiltonian Graphs, Digraphs, Trees, Algorithms, Paths, Planarity, and Chromatic Numbers. Applications such as Social Network Analysis will be stressed.

MAT 532. Geometry I. 3 Credits.

This course is a rigorous introduction to geometry from a transformational point of view, emphasizing Euclidean, affine, and projective geometry.

MAT 533. Geometry II. 3 Credits.

This course is a continuation of MAT 532. Topics covered include inversive geometry, hyperbolic geometry, and elliptic geometry from a transformational point of view.

MAT 535. Topology. 3 Credits.

This course is a rigorous introduction to point-set topology. Topics covered include topological spaces and continuous functions, connectedness, compactness, separation axioms, metrization theorems, and function spaces.

MAT 536. Algebraic Topology. 3 Credits.

This course is an introduction to the fundamental techniques of algebraic topology. Topics covered include fundamental groups and covering spaces, basic homological algebra, simplicial homology, singular homology, and cohomology.

MAT 536 Prerequisite: Successful completion of MAT 432 or MAT 535 or equivalent, with a minimum grade of C-.

MAT 543. Theory of Differential Equations. 3 Credits.

Existence and uniqueness theory, linear and nonlinear systems, elements of stability theory, and fundamental theory of classical partial differential equations.

MAT 543 Prerequisite: Successful completion of MAT 343 or equivalent, with minimum grade of C-, or permission of instructor.

MAT 545. Real Analysis I. 3 Credits.

This course provides a rigorous study of real-valued functions of a real variable. Topics include properties of the real numbers, convergence of sequences and series, basic topology of the real line, limits and continuity, the derivative and its applications, and the Riemann integral.

MAT 546. Real Analysis II. 3 Credits.

This course is a continuation of MAT 545. A central theme is the study of sequences and series of functions, with particular emphasis on the theory and applications of Taylor series and Fourier series. Additional topics, such as measure theory and the Lebesgue integral, may be explored as time permits.

MAT 546 Prerequisite: Successful completion of MAT 545, with a minimum grade of C-.

MAT 548. Industrial Mathematics - Continuous Models. 3 Credits.

A survey of mathematical concepts, techniques, and numerical algorithms used to study real-world mathematical models. Application areas include population dynamics, feedback and control systems, traffic flow, epidemiology, mathematical biology, physiology, queues, efficient call and traffic routing, and optimal scheduling. The software package MATLAB will be used in the analysis of problems.

MAT 548 Prerequisite: Successful completion of MAT 343 or equivalent, with a minimum grade of C-.

MAT 552. Operations Research. 3 Credits.

This course provides an overview of deterministic operations research methodology including linear, integer, nonlinear, and dynamic programming, and classical optimization problems. The computer algebra system MATLAB and other software will be used as an investigative tool in analyzing the problems that arise.

MAT 553. Stochastic Modeling. 3 Credits.

This course introduces topics in stochastic optimization and control (including Markov chains, queueing theory, reliability theory, inventory theory, and forecasting), discrete-event and Monte Carlo simulation, and stochastic differential equations. Applications are drawn from manufacturing, finance, logistics, and service systems. The computer algebra system MATLAB and other software will be used as an investigative tool in analyzing these models.

MAT 554. Scientific Computing. 3 Credits.

This course illustrates the use of numerical schemes and computing tools in multiple computational science domains. The focus is on numerical methods (including solutions of linear and nonlinear algebraic equations, solutions of ordinary and partial differential equations, finite differences, linear programming, optimization algorithms, and fast-Fourier transforms) and appropriate scientific programming skills to assist in investigating mathematical models of phenomena in the physical, ecological, and financial realms.

MAT 575. Complex Analysis I. 3 Credits.

This course covers basic properties of functions of a single complex variable. Topics include complex arithmetic, analytic functions and mappings, contour integrals, Cauchy's Theorem, Taylor and Laurent series, and the theory and application of residues.

MAT 595. Topics in Mathematics. 1-3 Credits.

Topics announced at time of offering.

Repeatable for credit.

MAT 599. Independent Study. 3 Credits.

Students will work independently on a mathematics topic of their choice under the aegis of a Mathematics Department faculty member.

MAT 609. Thesis I. 3 Credits.

Conduct literature search, develop thesis proposal and begin research under the guidance of a mathematics department faculty member.

MAT 610. Thesis II. 3 Credits.

This course is a continuation of MAT 609. The student will continue research under the guidance of a Mathematics Department faculty member and prepare their thesis for submission.